I, too, thought of making sort of a “fake” top of the door on the header. For one thing, the new doors are paneled steel on the outside with a 2” foam core on the inside. It would be a tough cut, and would probably never look right. The other 2 garage doors have already been replaced.
My bigger problem is the height. Shortening the door would also require that the door would have to be lower from the ceiling when opened. This garage is my shop. One of its uses is for auto projects, and the ceiling is already a little too low, especially when the car is up on the lift. Besides, I think I would also be hitting my head on it all the time.
I’ve actually thought up a solution of sorts. See what you think.
Since the garage is really deep, I am going to try mounting a regular garage door opener completely behind the door, so when the door is opened, the beginning of the opener’s track will be behind the door. This will not change the relationship between the way the opener moves, and the way the door moves. I will just have to fabricate a long rod to connect the opener to the door.